The actual term is "Cased-Hole" Logging not "Closed-Hole"....
There are two main types of wireline logging: Open-Hole & Cased-Hole...
Open-Hole where you obtain all the geologic/petrophysical data that can you the presence of hydrocarbons, the porosity, permeability, etc... But there is only one chance to get this data. If you case the hole without running open-hole wireline logs, all that valuable data is lost forever...
Cased-Hole logging can tell you how well your cement has bond to the casing, it can suggest fluid levels behind the casing. It can point to where there might be a hole in the casing, but it cannot tell you anything about the geology or presence of oil behind that casing...
I have never heard of an operating company drilling a well & not running open-hole logs before running casing. They will regret this decision, as the information obtained is priceless...